How could a country shift its production possibilities curve to the right through improved technology?

A worker in the United States and a worker in China can each produce 1,000 pairs of jeans per week. A worker in the United States can produce 50 cell phones in a week, and a worker in China can produce 100 cell phones in a week. Answer the following questions based on this information. Calculate the opportunity cost of producing jeans for each country.

In the picture below is the full question. The highlighted one is my guess which is wrong. Based on the production table above, what is the opportunity cost of 1 burger in 'Merica A) 1/3 of a burger B) 1/2 a burger(this one is wrong) C) 3 units of fries D) 2 units of fries

I've already read the answer provided on this site, but it is not giving me the information I need. I understand the math for finding the opportunity costs for each item in each country. However, where are they getting the answer that 2.5 tons of chemicals is what the US will give up, and 1 ton of apparel is what China will give up? From videos I've seen on youtube, they basically state that as long as the cost is less than what the original opportunity cost is, then nations will trade. So, it costs China 4 apparel for every 1 ton of chemicals, and in the US it costs 1 apparel for every 3 tons of chemicals. Am I right to assume that as long as China can trade less than 4 apparel it will benefit, and as long as the US can trade less than 3 tons of chemicals it will benefit? If so, then what is the math being used to arrive at exactly 1 ton of Chemicals for 1 ton of Apparel for China, and 1 apparel for 2.5 tons of Chemicals for the US? I need to understand the math that is used to…